X3291

INTERSECTION OF LINES X2X_39 AND X230X_231

Let L denote the line through X3 perpendicular to the line X2X6. Coefficients for a trilinear equation for L are the trilinears for X3291.
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 3124, 3231 }: Central Line L(3124, 3231) { 2, 39 }: Central Line L(2, 39) { 23, 111 }: Central Line L(23, 111) { 6, 373 }: Central Line L(6, 373) { 230, 231 }: Central Line L(230, 231) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_3124 = DANNEELS PERSPECTOR FOR X(76) (0.7888, 0.1151) X_3231 = ISOGONAL CONJUGATE OF X(3228) (1.4041, 1.1314) X_2 = CENTROID (0.5374, 0.2000) X_39 = BROCARD MIDPOINT (0.5778, 0.2305) X_23 = FAR-OUT POINT (1.3871, 2.4232) X_111 = PARRY POINT (0.9885, -0.0457) X_6 = SYMMEDIAN POINT (LEMOINE POINT, GREBE POINT) (0.6000, 0.2672) X_373 = CENTROID OF THE PEDAL TRIANGLE OF THE CENTROID (0.5614, 0.2395) X_230 = -CEVA CONJUGATE OF X(114) (0.9746, 0.6698) X_231 = -CEVA CONJUGATE OF X(128) (1.0375, 0.6458) X_3291 = INTERSECTION OF LINES X(2)X(39) AND X(230)X(231) (1.0965, 0.6233) A B C X3124 X3231 X2 X39 X23 X111 X6 X373 X230 X231 X3291 (a, b, c) = (5, 6, 7) | AB = 1

X3291 (INTERSECTION OF LINES X2X_39 AND X230X_231) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Trilinears: \(a(b^{4} + c^{4} + a^{2}b^{2} + a^{2}c^{2} - 4b^{2}c^{2}) : :\)
Search Value (6, 9, 13): \(-0.735156775295\)
▸ Alternate Coordinates2 forms

  • Trilinears: \((\sin 2A)(\sin^{2} A) \cos(A + \omega ) : :\)

  • Trilinears: \((\cos A)(\sin^{3} A) \cos(A + \omega ) : :\)

▸ Incident Central Lines10 lines

{2, 39}, {6, 373}, {23, 111}, {25, 1611}, {32, 1995}, {51, 1613}, {110, 1692}, {115, 858}, {230, 231}, {325, 1570}

▸ Functional Relations13 relations